Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import math
n=int(input())
x=int(math.sqrt(n))
l=x
r=x
first=0
if(l*(l+1)+r*(r+1)==2*n or ((l-1)*l+(r-1)*r)==2*n):
##	print "SDF"
	print "YES"
else:
	while(l>0):
		if((l*(l+1) + r*(r+1))> 2*n):
			l-=1
		elif((l*(l+1) + r*(r+1))< 2*n):
			r+=1
		else:
			first=1
			print "YES"
			break

	if(first==0):
		print "NO"